The parametric study yields stable equilibria up to a normalized helicity of \(H/F^2=0.25\) , which, to our knowledge, is higher than what has been found so far [1]}. For this equilibrium, the ratio of the flux in the current channel to the external poloidal flux, \(\mathcal {R}=F_\mathrm {cc}/F_\mathrm {ep}=0.94\) , is significantly higher than previous estimates of the limiting flux ratio, which lie in the range of \(\sim \!0.1\mbox{--}0.5\)  [2]}, [3]}, [4]}. The corresponding ratio of self (current-carrying) helicity to total helicity is \(H_\mathrm {self}/H=0.315\) , which is only slightly higher than a previously suggested limit of \(\simeq 0.29\pm 0.01\)  for torus-unstable flux ropes [5]}, but lower than a limit of \(\sim \!0.45\)  for eruptions from newly emerging flux [6]}.
